The sum of two numbers is $84$, and their difference is $6$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 84}$ ${x-y = 6}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 90 $ $ x = \dfrac{90}{2} $ ${x = 45}$ Now that you know ${x = 45}$ , plug it back into $ {x+y = 84}$ to find $y$ ${(45)}{ + y = 84}$ ${y = 39}$ You can also plug ${x = 45}$ into $ {x-y = 6}$ and get the same answer for $y$ ${(45)}{ - y = 6}$ ${y = 39}$ Therefore, the larger number is $45$, and the smaller number is $39$.